The invention relates to an apparatus for stacking thin flexible objects, particularly sheets of paper in either the folded or unfolded state. Generally rudimentary means are used for stacking thin objects, e.g. in the form of a rack with a sloping bottom and using the action of gravity. Due to their natural velocity and once released by the handling system the objects abut against the front wall of the rack at the same time as they drop on to the stack being formed. However, there are serious limitations to the efficiency of such stacking procedures. Thus, the reliability of stacking is uncertain at the high supply speed and more particularly in the case of previously folded sheets. The sheets may stick together and they are not satisfactorily arranged on the stack.